> What kind of project would be a sweet spot to ATS?
I'd say a large mission-critical C codebase that decides to grow and expand a formally-verified kernel of its most important functionality - it can be a real-time sytem, an OS kernel, a HFT algorithm etc.
Nowadays people seem excited about gradual typing in widespread dynamic languages like JavaScript and Python, because it allows them to adopt the best parts of static typing without having to rewrite the entire codebases in new langauges. Now imagine that you can introduce gradual formal verification to your battle-tested C codebase, without a loss in performance[1] and without forcing you into a new tooling ecosystem (compiler, debugger, profiler etc). Actually, you don't need to imagine it, because that's what ATS is :)
> I would love to understand the nature of the theoretical advantage ATS has here over Rust.
I'd say it's a synergy of two key features, that produce miracles when put together - 1) direct and safe pointer arithmetics [2], which enables the same data structures and optimisation tricks available in C, yet in a verifiable environment, and 2) refinement types [3].
> Would it be comparible with F*
Unfortunately, I don't know much about F*, MS Research regularly releases a new PL prototype after the other and I lost my count on Koka[4].
> ATS seems to be very much a concept/language in R&D phase. Its ergononics are difficult ergonomics (have a look at the error messages), documentation and example projects sparse
All true, but nonetheless it's a solid implementation of the mentioned theoretical parts, and if one dares to get through the objective lack of docs and ambigouos compiler messages, they are rewarded with an impressively powerful production-ready system-level compiler, complimentary to their standard C ecosystem which has decades of accumulated wisdom. That's the level of code-reuse other ecosystems can only dream of.
[1] http://blog.vmchale.com/article/ats-performance
[2] http://blog.vmchale.com/article/ats-safe-pointers
[3] http://ats-lang.github.io/DOCUMENT/INT2PROGINATS/HTML/c2584....
[4] https://www.microsoft.com/en-us/research/project/koka/